1. **State the problem:** Find the midpoint of the line segment joining the points (8, -6) and (4, 5). 2. **Formula:** The midpoint $M$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 3. **Apply the formula:** Substitute $x_1=8$, $y_1=-6$, $x_2=4$, and $y_2=5$: $$M = \left( \frac{8 + 4}{2}, \frac{-6 + 5}{2} \right)$$ 4. **Simplify each coordinate:** $$M = \left( \frac{12}{2}, \frac{-1}{2} \right)$$ 5. **Calculate the values:** $$M = (6, -0.5)$$ **Final answer:** The midpoint coordinate is $\boxed{(6, -0.5)}$.